6,732 research outputs found
Automorphism groups of polycyclic-by-finite groups and arithmetic groups
We show that the outer automorphism group of a polycyclic-by-finite group is
an arithmetic group. This result follows from a detailed structural analysis of
the automorphism groups of such groups. We use an extended version of the
theory of the algebraic hull functor initiated by Mostow. We thus make
applicable refined methods from the theory of algebraic and arithmetic groups.
We also construct examples of polycyclic-by-finite groups which have an
automorphism group which does not contain an arithmetic group of finite index.
Finally we discuss applications of our results to the groups of homotopy
self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of
arithmeticity results of Sullivan in rational homotopy theory
AdS Strings with Torsion: Non-complex Heterotic Compactifications
Combining the effects of fluxes and gaugino condensation in heterotic
supergravity, we use a ten-dimensional approach to find a new class of
four-dimensional supersymmetric AdS compactifications on almost-Hermitian
manifolds of SU(3) structure. Computation of the torsion allows a
classification of the internal geometry, which for a particular combination of
fluxes and condensate, is nearly Kahler. We argue that all moduli are fixed,
and we show that the Kahler potential and superpotential proposed in the
literature yield the correct AdS radius. In the nearly Kahler case, we are able
to solve the H Bianchi using a nonstandard embedding. Finally, we point out
subtleties in deriving the effective superpotential and understanding the
heterotic supergravity in the presence of a gaugino condensate.Comment: 42 pages; v2. added refs, revised discussion of Bianchi for N
Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds
In this paper, we numerically investigate the length spectra and the
low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large
number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero
eigenvalues have been successfully computed using the periodic orbit sum
method, which are compared with various geometric quantities such as volume,
diameter and length of the shortest periodic geodesic of the manifolds. The
deviation of low-lying eigenvalue spectra of manifolds converging to a cusped
hyperbolic manifold from the asymptotic distribution has been measured by
function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of
cusped manifolds in section 2 is correcte
Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories
We generalize the Schwinger model on the lattice by adding a charged
scalar field. In this so-called model the scalar field shields
the fermion charge, and a neutral fermion, acquiring mass dynamically, is
present in the spectrum. We study numerically the mass of this fermion at
various large fixed values of the gauge coupling by varying the effective
four-fermion coupling, and find an indication that its scaling behavior is the
same as that of the fermion mass in the chiral Gross-Neveu model. This suggests
that the model is in the same universality class as the
Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary
strong gauge coupling.Comment: 18 pages, LaTeX2e, requires packages rotating.sty and curves.sty from
CTA
Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representation
We present here an augmented space recursive technique in the
k-representation which include diagonal, off-diagonal and the environmental
disorder explicitly : an analytic, translationally invariant, multiple
scattering theory for phonons in random binary alloys.We propose the augmented
space recursion (ASR) as a computationally fast and accurate technique which
will incorporate configuration fluctuations over a large local environment. We
apply the formalism to , Ni_{88}Cr_12} and
alloys which is not a random choice. Numerical results on spectral functions,
coherent structure factors, dispersion curves and disordered induced FWHM's are
presented. Finally the results are compared with the recent itinerant coherent
potential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure
Different HLA-DRB1 allele distributions in distinct clinical subgroups of sarcoidosis patients
<p>Abstract</p> <p>Background</p> <p>A strong genetic influence by the MHC class II region has been reported in sarcoidosis, however in many studies with different results. This may possibly be caused by actual differences between distinct ethnic groups, too small sample sizes, or because of lack of accurate clinical subgrouping.</p> <p>Subjects and methods</p> <p>In this study we HLA typed a large patient population (n = 754) recruited from one single centre. Patients were sub-grouped into those with Löfgren's syndrome (LS) (n = 302) and those without (non-Löfgren's) (n = 452), and the majority of them were clinically classified into those with recovery within two years (resolving) and those with signs of disease for more than two years (non-resolving). PCR was used for determination of HLA-DRB1 alleles. Swedish healthy blood donors (n = 1366) served as controls.</p> <p>Results</p> <p>There was a dramatic difference in the distribution of HLA alleles in LS compared to non-LS patients (p = 4 à 10<sup>-36</sup>). Most notably, DRB1*01, DRB1*03 and DRB1*14, clearly differed in LS and non-LS patients. In relation to disease course, DRB1*07, DRB1*14 and DRB1*15 generally associated with, while DRB1*01 and DRB1*03 protected against, a non-resolving disease. Interestingly, the clinical influence of DRB1*03 (good prognosis) dominated over that of DRB1*15 (bad prognosis).</p> <p>Conclusions</p> <p>We found several significant differences between LS and non-LS patients and we therefore suggest that genetic association studies in sarcoidosis should include a careful clinical characterisation and sub-grouping of patients, in order to reveal true genetic associations. This may be particularly accurate to do in the heterogeneous non-LS group of patients.</p
Expansion in perfect groups
Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an
integer q, denote by Ga_q the subgroup of Ga consisting of the elements that
project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q
with respect to the generating set S form a family of expanders when q ranges
over square-free integers with large prime divisors if and only if the
connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas
are explained in more details in the introduction, typos corrected, results
and proofs unchange
Direct replacement of oral sodium benzoate with glycerol phenylbutyrate in children with urea cycle disorders
Long-term management of urea cycle disorders (UCDs) often involves unlicensed oral sodium benzoate (NaBz) which has a high volume and unpleasant taste. A more palatable treatment is licenced and available (glycerol phenylbutyrate [GPB], Ravicti) but guidance on how to transition patients from NaBz is lacking. A retrospective analysis of clinical and biochemical data was performed for eight children who transitioned from treatment with a single ammonia scavenger, NaBz, to GPB at a single metabolic centre; UCDs included arginosuccinic aciduria (ASA) (n = 5), citrullinaemia type 1 (n = 2) and carbamoyl phosphate synthetase I deficiency (CPS1) (n = 1). Patients transitioned either by gradual transition over 1â2 weeks (n = 3) or direct replacement of NaBz with GPB (n = 5). Median initial dose of GPB was 8.5 mL/m2/day based on published product information; doses were revisited subsequently in clinic and titrated individually (range 4.5â11 mL/m2/day). Pre-transition and post-transition mean ammonia levels were 37 ÎŒmol/L (SD 28 ÎŒmol/L) and 29 ÎŒmol/L (SD 22 ÎŒmol/L), respectively (p = 0.09), and mean glutamine levels were 664 ÎŒmol/L (SD 225 ÎŒmol/L) and 598 ÎŒmol/L (SD 185 ÎŒmol/L), respectively (p = 0.24). There were no reductions in levels of branched chain amino acids. No related adverse drug reactions were reported. Patients preferred GPB because of its lower volume and greater palatability. Direct replacement of NaBz with GPB maintained metabolic control and was simple for the health service and patients to manage. A more cautious approach with additional monitoring would be warranted in brittle patients and patients whose ammonia levels are difficult to control
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